3 Dottore di ricerca 2013 - 2019

Pubblicazioni 2006-2019

• 2019
  • S. Graillat, F. Jézéquel, R. Picot, F. Févotte, B. Lathuilière : “Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic”, Journal of Computational Science (2019)
  • R. Iakymchuk, S. Graillat, D. Defour, E. Quintana‑Ortí : “Hierarchical approach for deriving a reproducible unblocked LU factorization”, International Journal of High Performance Computing Applications, pp. #1094342019832968 (2019)
  • S. Graillat, F. Jézéquel : “Tight interval inclusions with compensated algorithms”, IEEE Transactions on Computers, pp. 1-10 (2019)
• 2018
  • S. Graillat : “An accurate algorithm for evaluating rational functions”, Applied mathematics and computation, vol. 337, pp. 494-503 (2018)
  • S. Graillat : “An accurate algorithm for evaluating rational functions”, Applied Mathematics and Computation, vol. 337, pp. 494-503, (Elsevier) (2018)
  • S. Graillat, F. Jézéquel, R. Picot : “Numerical Validation of Compensated Algorithms with Stochastic Arithmetic”, Applied Mathematics and Computation, vol. 329, pp. 339-363, (Elsevier) (2018)
  • S. Graillat, F. Jézéquel, R. Picot, F. Févotte, B. Lathuilière : “Numerical validation in quadruple precision using stochastic arithmetic”, TNC'18. Minisymposium on Trusted Numerical Computations. International Conference on Emerging Trends in Applied Mathematics and Mechanics, vol. 8, Kalpa Publications in Computing, Krakow, Poland, pp. 38-53, (EasyChair) (2018)
  • S. Graillat, F. Jézéquel : “Tight interval inclusions with compensated algorithms”, 18^th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2018), 18^th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2018), Book of Abstracts, Tokyo, Japan, pp. 86-87 (2018)
• 2017
  • S. Graillat, C. Jeangoudoux, Ch. Lauter : “MPDI: A Decimal Multiple-Precision Interval Arithmetic Library”, Reliable Computing Journal, vol. 25, pp. 38-52 (2017)
  • S. Boldo, S. Graillat, J.‑M. Muller : “On the robustness of the 2Sum and Fast2Sum algorithms”, ACM Transactions on Mathematical Software, vol. 44 (1), (Association for Computing Machinery) (2017)
  • Lokman A. Abbas‑Turki, S. Graillat : “Resolution of a large number of small random symmetric linear systems in single precision arithmetic on GPUs”, Journal of Supercomputing, vol. 73 (4), pp. 1360-1386, (Springer Verlag) (2017)
  • S. Graillat, Y. Ibrahimy, C. Jeangoudoux, Ch. Lauter : “A Parallel Compensated Horner Scheme”, CSE 2017, SIAM Conference on Computational Science and Engineering (CSE), Atlanta, USA (2017)
  • S. Graillat : “Accurate computations with polynomials”, The International Workshop on Numerical Verification and its Applications, Miyako-jima, Okinawa, Japan (2017)
  • R. Iakymchuk, S. Graillat, D. Defour, E. Laure, E. Quintana‑Ortí : “Towards a Reproducible Solution of Linear Systems”, Supercomputing Conference 2017-Computational Reproducibility at Exascale Workshop, Denver, USA (2017)
  • R. Iakymchuk, E. Quintana‑Ortí, E. Laure, S. Graillat : “Towards Reproducible Blocked LU Factorization”, 4^th International Workshop on Reproducibility in Parallel Computing in conjunction with IPDPS 2017 - 31^st IEEE International Parallel & Distributed Processing Symposium, Orlando, USA (2017)
• 2016
  • H. Jiang, S. Graillat, R. Barrio, C. Yang : “Accurate, validated and fast evaluation of elementary symmetric functions and its application”, Applied Mathematics and Computation, vol. 273, pp. 1160-1178, (Elsevier) (2016)
  • S. Graillat, F. Jézéquel, M. Ibrahim : “Dynamical control of Newton’s method for multiple roots of polynomials”, Reliable Computing Journal, vol. 21 (2016)
  • P. Fortin, M. Gouicem, S. Graillat : “GPU-Accelerated Generation of Correctly Rounded Elementary Functions”, ACM Transactions on Mathematical Software, vol. 43 (3), pp. 22:1-22:26, (Association for Computing Machinery) (2016)
  • R. Iakymchuk, I. Toshiyuki, S. Graillat, S. Markidis, E. Laure : “A Case Study of the Reproducibility Issues in EigenExa”, EASC2016, Exascale Applications and Software Conference, Stockholm, Sweden (2016)
  • S. Graillat, C. Jeangoudoux, Ch. Lauter : “A Decimal Multiple-Precision Interval Arithmetic Library”, 17^th International Symposium on Scientific Computing, Computer Arithmetics and Verified Numerics. , Uppsala, Sweden (2016)
  • R. Iakymchuk, S. Graillat, D. Defour, E. Quintana‑Ortí : “Hierarchical Approach for Deriving a Reproducible LU factorization on GPUs”, The Numerical Reproducibility at Exascale (NRE16) workshop held as part of the Supercomputing Conference (SC16), Salt Lake City, UT, USA (2016)
  • S. Graillat, F. Jézéquel, R. Picot, F. Févotte, B. Lathuilière : “PROMISE: floating-point precision tuning with stochastic arithmetic”, 17^th international symposium on Scientific Computing, Computer Arithmetic and Verified Numerics (SCAN 2016), UPPSALA, Sweden, pp. 98-99 (2016)
  • R. Iakymchuk, D. Defour, S. Collange, S. Graillat : “Reproducible and Accurate Algorithms for Numerical Linear Algebra”, PP: Parallel Processing for Scientific Computing, Paris, France, (SIAM) (2016)
  • L.A. Abbas‑Turki, S. Graillat : “Resolution of a large number of small random symmetric linear systems in single precision arithmetic on GPUs”, International conference on Monte-Carlo techniques, Paris, France, pp. 25 (2016)
  • R. Iakymchuk, D. Defour, S. Graillat : “Towards Fast, Accurate and Reproducible LU Factorization”, SCAN 2016, 17^th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, Uppsala, Sweden, pp. 59-60 (2016)
• 2015
  • S. Graillat, Ch. Lauter, P. Peter Tang, N. Yamanaka, Sh. Oishi : “Efficient Calculations of Faithfully Rounded l2-Norms of n-Vectors”, ACM Transactions on Mathematical Software, vol. 41 (4), pp. 24:1, (Association for Computing Machinery) (2015)
  • S. Collange, D. Defour, S. Graillat, R. Iakymchuk : “Numerical Reproducibility for the Parallel Reduction on Multi- and Many-Core Architectures”, Parallel Computing, vol. 49, pp. 83-97 (2015)
  • S. Graillat, V. Lefèvre, J.‑M. Muller : “On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic”, Numerical Algorithms, vol. 70 (3), pp. 653-667, (ISBN: 1017-1398) (2015)
  • R. Iakymchuk, S. Graillat, S. Collange, D. Defour : “ExBLAS: Reproducible and Accurate BLAS Library”, RAIM: Rencontres Arithmétiques de l'Informatique Mathématique, Rennes, France (2015)
  • R. Iakymchuk, S. Collange, D. Defour, S. Graillat : “ExBLAS: Reproducible and Accurate BLAS Library”, NRE: Numerical Reproducibility at Exascale, Austin, TX, United States (2015)
  • S. Graillat, F. Jézéquel, R. Picot : “Numerical validation of compensated summation algorithms with stochastic arithmetic”, 8^th International Workshop on Numerical Software Verification, NSV 2015, vol. 317, Electronic Notes in Theoretical Computer Science, Seattle, USA, pp. 55-69, (Elsevier) (2015)
  • R. Iakymchuk, S. Collange, D. Defour, S. Graillat : “Reproducibility and Accuracy for High-Performance Computing”, RAIM: Rencontres Arithmétiques de l’Informatique Mathématique, Rennes, France (2015)
  • R. Iakymchuk, D. Defour, S. Collange, S. Graillat : “Reproducible Triangular Solvers for High-Performance Computing”, ITNG: Information Technology - New Generations, Las Vegas, NV, United States, pp. 353-358 (2015)
  • R. Iakymchuk, D. Defour, S. Collange, S. Graillat : “Reproducible and Accurate Matrix Multiplication for GPU Accelerators”, (2015)
  • R. Iakymchuk, D. Defour, S. Collange, S. Graillat : “Reproducible Triangular Solvers for High-Performance Computing”, (2015)
• 2014
  • S. Graillat, Ch. Lauter, P. Peter Tang, N. Yamanaka, Sh. Oishi : “A method of calculating faithful rounding of l2-norm for n-vectors”, 16^th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computation (SCAN), Wuerzburg, Germany, pp. 60-61 (2014)
  • S. Collange, D. Defour, S. Graillat, R. Iakymchuk : “A Reproducible Accurate Summation Algorithm for High-Performance Computing”, EX: Exascale Applied Mathematics Challenges and Opportunities, Chicago, USA (2014)
  • R. Iakymchuk, D. Defour, S. Collange, S. Graillat : “Reproducible and Accurate Matrix Multiplication”, SCAN: Scientific Computing, Computer Arithmetic and Validated Numerics n°9553, Lecture Notes of Computer Science, Wurzburg, Germany, pp. 126-137 (2014)
  • S. Collange, D. Defour, S. Graillat, R. Iakymchuk : “Reproducible and Accurate Matrix Multiplication for High-Performance Computing”, SCAN: Scientific Computing, Computer Arithmetic and Validated Numerics, Wuerzburg, Germany, pp. 42-43 (2014)
  • S. Collange, D. Defour, S. Graillat, R. Iakymchuk : “Full-Speed Deterministic Bit-Accurate Parallel Floating-Point Summation on Multi- and Many-Core Architectures”, Sorbonne Universites, UPMC Univ Paris 06, UMR 7606, LIP6, F-75005 Paris, France (2014)
• 2013
  • H. Jiang, S. Graillat, C. Hu, Sh. Lia, X. Liao, L. Cheng, F. Su : “Accurate evaluation of the $k$-th derivative of a polynomial”, Journal of Computational and Applied Mathematics, vol. 243, pp. 28-47, (ISBN: 0377-0427) (2013)
  • H. Jiang, S. Graillat, R. Barrio : “Accurate and Fast Evaluation of Elementary Symmetric Functions”, 21^st IEEE Symposium on Computer Arithmetic, ARITH 2013, Austin, TX, USA, pp. 183-190, (IEEE) (2013)
  • S. Graillat : “Contribution to the increase of accuracy and validation of numerical algorithms”, abilitazione, difesa 12/02/2013 (2013)
• 2012
  • S. Graillat, V. Ménissier‑Morain : “Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic”, Information and Computation n°216, pp. 57-71, (ISBN: 0890-5401) (2012)
  • P. Fortin, M. Gouicem, S. Graillat : “Solving the Table Maker’s Dilemma by reducing divergence on GPU”, Proceedings of the 15^th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations, Novosibirsk, Russia, pp. 45-46 (2012)
  • P. Fortin, M. Gouicem, S. Graillat : “Towards solving the Table Maker’s Dilemma on GPU”, 20^th Euromicro International Conference on Parallel, Distributed and Network-based Processing, Garching, Germany, pp. 407-415, (IEEE) (2012)
• 2011
  • S. Graillat, F. Jézéquel, Sh. Wang, Y. Zhu : “Stochastic Arithmetic in Multiprecision”, Mathematics in Computer Science, vol. 5 (4), pp. 359-375, (ISBN: 1661-8270) (2011)
• 2010
  • S. Graillat, F. Jézéquel, Y. Zhu : “SAM: a multiprecision stochastic arithmetic library”, 14^th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2010), Lyon, France, pp. 70-71 (2010)
  • S. Graillat, F. Jézéquel, Y. Zhu : “Stochastic Arithmetic in Multiprecision”, Third International Workshop on Numerical Software Verification (NSV-3), part of Federated Logic Conference (FLoC), Edinburgh, United Kingdom (2010)
  • J. Jean, S. Graillat : “Fast dot product over finite field”, (2010)
• 2009
  • S. Graillat : “Accurate Floating Point Product and Exponentiation”, IEEE Transactions on Computers, vol. 58 (7), pp. 994-1000, (Institute of Electrical and Electronics Engineers) (2009)
  • S. Graillat, Ph. Langlois, N. Louvet : “Algorithms for Accurate, Validated and Fast Polynomial Evaluation”, Japan Journal of Industrial and Applied Mathematics, vol. 26 (2-3), pp. 191-214 (2009)
  • H. Nguyen, S. Graillat, J.‑L. Lamotte : “Extended precision with a rounding mode toward zero environment. Application on the CELL processor”, International Journal of Reliability and Safety, vol. 3 (1-3), pp. 153-173, (ISBN: 1479-389X) (2009)
  • S. Graillat, Ph. Trébuchet : “A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system”, ISSAC'09 - the 2009 international symposium on Symbolic and algebraic computation, Seoul, South Korea, pp. 167-173, (ACM) (2009)
  • J.‑M. Chesneaux, S. Graillat, F. Jézéquel : “Rounding errors”, chapter in Wiley Encyclopedia of Computer Science and Engineering (Benjamin Wah, ed.), vol. 4, B. Wah (Ed.), Hoboken, N.J., pp. 2490-2494, (ISBN: 978-0-471-38393-2) (2009)
  • J.‑M. Chesneaux, S. Graillat, F. Jézéquel : “Numerical validation and assessment of numerical accuracy”, LIP6 (2009)
• 2008
  • S. Graillat : “Accurate simple zeros of polynomials in floating point arithmetic”, Computers and Mathematics with Applications, vol. 56 (4), pp. 1114-1120, (ISBN: 0898-1221) (2008)
  • S. Graillat : “Some topological and geometric properties of pseudozero set”, Applied Mathematics E-Notes, vol. 8, pp. 98-108, (ISBN: 1607-2510) (2008)
  • S. Graillat : “Accurate Floating Point Product”, Proceedings of the Workshop on Reliable Engineering Computing, Savannah, Georgia, USA, pp. 351-361 (2008)
  • S. Graillat : “Accurate simple zeros of polynomials”, 13^th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations SCAN'08, El Paso, Texas, USA, pp. 52-53 (2008)
  • S. Graillat, V. Ménissier‑Morain : “Compensated Horner scheme in complex floating point arithmetic”, Proceedings, 8^th Conference on Real Numbers and Computers, J. D. Bruguera, D. Daumas (Eds.), Santiago de Compostela, Spain, pp. 133-146, (ISBN: 978-84-691-4381-0) (2008)
  • S. Graillat, J.‑L. Lamotte, H. Nguyen : “Error-Free Transformation in Rounding Mode toward Zero”, Numerical Validation in Current Hardware Architectures, revised papers, vol. 5492, Lecture Notes In Computer Science, Dagstuhl, Germany, pp. 217-229, (Springer) (2008)
  • S. Graillat, J.‑L. Lamotte, Siegfried M. Rump, S. Markov : “Interval arithmetic on the Cell processor”, 13^th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations SCAN'08, El Paso, Texas, USA, pp. 54-54 (2008)
  • H. Nguyen, S. Graillat, J.‑L. Lamotte : “Precise and effective scientific calculation on the CELL processor”, Proceedings of the Workshop on Reliable Engineering Computing, Savannah, Georgia, USA, pp. 333-350 (2008)
• 2007
  • S. Graillat : “Pseudozero Set of Real Multivariate Polynomials”, Mathematics in Computer Science, vol. 1 (2), pp. 337-352, (ISBN: 1661-8270) (2007)
  • S. Graillat, Ph. Langlois : “Real and complex pseudozero sets for polynomials with applications”, RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), vol. 41 (1), pp. 45-56, (ISBN: 0988-3754) (2007)
  • S. Graillat, V. Ménissier‑Morain : “Error-Free Transformations in Real and Complex Floating Point Arithmetic”, Proceedings of International Symposium on Nonlinear Theory and its Applications (NOLTA'07), Vancouver, Canada, pp. 341-344 (2007)
• 2006
  • S. Graillat : “A note on structured pseudospectra”, Journal of Computational and Applied Mathematics, vol. 191 (1), pp. 68-76, (ISBN: 0377-0427) (2006)
  • F. Tisseur, S. Graillat : “Structured condition numbers and backward errors in scalar product spaces”, Electronic Journal of Linear Algebra, vol. 15, pp. 159-177, (ISBN: 1081-3810) (2006)
  • S. Graillat, Ph. Langlois, N. Louvet : “Choosing a twice more accurate dot product implementation”, ICNAAM: International Conference of Numerical Analysis and Applied Mathematics, Hersonnisos, Crete, Greece, pp. 498-499 (2006)
  • S. Graillat : “Validated Pseudozero Set of Polynomials”, 12^th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, Duisburg, Germany, Duisburg, Germany, pp. 160-161, (IEEE) (2006)